41 citations · 54 across the 7 of their papers we have counts for
7 papers
Fractional Poisson Fields and Martingales
Giacomo Aletti, Nikolai Leonenko, Ely Merzbach
We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given.…
The set-indexed Lévy process: Stationarity, Markov and sample paths properties
Erick Herbin, Ely Merzbach
We present a satisfactory definition of the important class of Lévy processes indexed by a general collection of sets. We use a new definition for increment stationarity of set-ind…
Optimal detection of a change-set in a spatial Poisson process
B. Gail Ivanoff, Ely Merzbach
We generalize the classic change-point problem to a "change-set" framework: a spatial Poisson process changes its intensity on an unobservable random set. Optimal detection of the…
Stationarity and Self-similarity Characterization of the Set-indexed Fractional Brownian Motion
Erick Herbin, Ely Merzbach
The set-indexed fractional Brownian motion (sifBm) has been defined by Herbin-Merzbach (2006) for indices that are subsets of a metric measure space. In this paper, the sifBm is pr…
A Characterization of the Set-indexed Fractional Brownian Motion by Increasing Paths
Erick Herbin, Ely Merzbach
We prove that a set-indexed process is a set-indexed fractional Brownian motion if and only if its projections on all the increasing paths are one-parameter time changed fractional…
The Multiparameter Fractional Brownian Motion
Erick Herbin, Ely Merzbach
We define and study the multiparameter fractional Brownian motion. This process is a generalization of both the classical fractional Brownian motion and the multiparameter Brownian…